2.MD.B.6 - About the Math, Learning Targets, and Increasing Rigor

Grade 2 Measurement and Data

2.MD.B.6

About the Math

Full Standard

Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.

Measurement Topic

This standard is reported on the report card in these quarters as follows:

**2nd Grade Students Learning 2nd Grade Standards**
Quarter 1	Quarter 2	Quarter 3	Quarter 4
Report Card Measurement Topic: Demonstrates understanding of number concepts and relationships

**1st Grade Students Learning 2nd Grade Standards**
Quarter 1	Quarter 2	Quarter 3	Quarter 4
Report Card Measurement Topic: Demonstrates understanding of number concepts and relationships

About the Math

Measure Skills and concepts below are learning goals for this standard.

A number line is a useful tool for adding and subtracting whole numbers and fractions. A ruler is a tool built around this concept. This standard should be integrated with computational standards in grade 2. Students should have experiences with an equally partitioned number line before transitioning to an empty (or open) number line.

Create a number line with whole number intervals (equal spacing).

Students should have experiences with an equally partitioned number line before transitioning to an empty (or open) number line.

Represent whole numbers on a number line.

Students should be able to identify and place numbers on a number line with given endpoints. At first, those endpoints should be static, common endpoints such as 0 and 100, 0 and 1,000, or 0 and 50. In time, students should begin to work with number lines using varied endpoints.

Represent a whole number on two different number lines that have different endpoints (e.g. place 80 on a number line that has endpoints of 0 and 100 and 50 and 100).

As students develop an understanding of larger numbers on number lines, we should begin to modify the number lines. Essentially, students need to understand that a number line shows the relationship between numbers. Number lines can have any endpoints. Students should understand that the position of a number changes as the endpoints change. For example, 50 is halfway between 0 and 100 but shifts considerably to the left when those endpoints change to 0 and 1,000 and 50 isn't on a number line with the endpoints of 75 and 90.

Find sums and differences within 100 using a number line.

A number line can be used to add and subtract. Students should first add and subtract with a ticked number line before seeing the relationships between ticked and open number lines. In time, students can then work with open number lines. Also, note that students should be able to add and subtract on a number line with varied endpoints. For example, when solving 43 + 35 students shouldn't have to jump from 0 to 43 before adding on 35. Instead, they should be able to start with 43 on the left endpoint.

Essential vocabulary for this standard includes length, unit, number line, sums, differences, measure, and distance.

Progression of Standard within Grade 2

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1	Quarter 2	Quarter 3	Quarter 4
Create a number line with whole number intervals (equal spacing). Represent whole numbers on a number line. Represent a whole number on two different number lines that have different endpoints (e.g. place 80 on a number line that has endpoints of 0 and 100 and 50 and 100). Find sums and differences within 100 using a number line.

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades
Grade	Grade 3
This concept is not taught prior to grade 2.	Understand a fraction as a number on the number line (3.NF.2)

Instructional Tasks

TASKS

These tasks can be used with small group or whole group instruction.

Draw an equally partitioned number line with tick marks to represent problems such as 5 + 3 or 6 - 2. It may be helpful to use lined paper. Rotate the paper so the blue lines can help equally partition the number line. Students could also solve problems such as 26 + 5 by starting at 26 and counting on 5 more.
Draw an equally partitioned number line with tick marks to represent a problem with two two-digit numbers that have a difference of 5.
Draw an equally partitioned number line with tick marks to show all the numbers between 36 and 42. This could be extended to also show the numbers between 98 and 103 and 242 and 248.
Display a number line that shows jumps on a number line and have students identify the equation. You could use this resource Links to an external site. to project a number line and show jumps. The equation for the number line below could be 38 + 49 = 87.
Look at the number line to the right. What numbers could might the letters A, B, C, and D represent? Explain your thinking.

Have students place the number 60 on a number line with endpoints of 50 and 70. Then, have them place the number 60 on a number line with endpoints of 0 and 100. How does changing the endpoints affect where 60 is placed? Why is it not in the same place on each number line?
Give students an empty number line. Provide them with a number (or students can use place value dice or digit cards). Students have to create their own end points and place the number you provided appropriately on the number line.
Give students a number line with endpoints. The student has to determine the midpoint and then choose a number less than/greater than the midpoint and place it appropriately on the number line.
Give students an empty number line with one point plotted somewhere on it, say 78. Ask students to pick and label appropriate endpoints based on where 78 is located.
Give students an open number line and have them solve problems such as 34 + 48. Problems can also be set in context. Chloe has 43 rocks and Shelly gives Chloe 48 more. How many rocks does Chloe have?

SLIDE-BASED TASKS

These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Module 2 • Place Value

Represent Whole Numbers on a Number Line:

Additional Tasks

These links provide ideas for lessons connected to this standard. [NOTE: NCTM membership required for access to Illuminations lessons.]

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Frog and Toad on the number line Links to an external site.(Illustrative Math)
Cupcake Mixup Download Cupcake Mixup
(Utah Core Academy lesson)
What Number Am I? Download What Number Am I?
(HCPSS)
Endpoint Download Endpoint
(HCPSS)
How Far? Download How Far?
(HCPSS)
Investigating Number Lines Teacher Directions Download Investigating Number Lines Teacher Directions
(HCPSS)
Investigating Number Lines Teaching Resource Download Investigating Number Lines Teaching Resource
(HCPSS)
Macaroni Math: Where Will I Land? Links to an external site. (NCTM Illuminations lesson plan)
Using the Number Line to Compare Links to an external site. (NCTM Illuminations lesson plan)
Additional Number Lines Download Additional Number Lines
(HCPSS)

Tasks From Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.

Print Resources
Book Title	Grade	Pages
Teaching Student-Centered Mathematics	K-3	231 (Guess and Measure, Activity 8.5) 247 (Personal Benchmarks, Activity 8.9) 229 (Crooked Paths, Activity 8.3)
Hands-On Standards	1-2	106-107 (Standard Units) 108-109 (Inches and Feet) 110-111 (Choosing a Unit)
Groundworks: Reasoning About Measurement	2	64-70 (Make Two Feet) 83-85 (Who am I?) 56-62 (Make a Yard,Grade 3 book)
Brain-Compatible Lessons for Mathematics	2-3	82-85 (Measuring Tools) 89-91 (Me and My Shadow)

Independent Work

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

Froggy Jumps of 10 Download Froggy Jumps of 10
(HCPSS-adapted resource)
Number Line Addition and Subtraction Download Number Line Addition and Subtraction
(HCPSS-adapted resource)

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

Assessment

Full Standard

Measurement Topic

The standard is reported on the report card through these measurement topics. Expand the measurement topic for a description of what students who meet expectation are able to do.

2nd Grade Students Learning 2nd Grade Standards by Measurement Topic

Demonstrates understanding of number concepts and relationships

Quarter 1

Represent whole numbers on an equally partitioned number line starting with 0.

1st Grade Students Learning 2nd Grade Standards by Measurement Topic

Demonstrates understanding of number concepts and relationships

Quarter 1

Represent whole numbers on an equally partitioned number line starting with 0.

2MD6 Anecdotal Data Recording Sheet Links to an external site.

Visit the SBIR (Standards Based Instruction and Reporting) page in Course Essentials for more information and clarification.

Rubric (for thinking and reasoning evidence)

Use this rubric for observation and constructed responses (tasks that require explanation, justification, and/or representation).

Rubric for Tasks (pdf) Links to an external site.

Exemplars for this standard

Use the links below to access a task for this standard as well as student work samples that are examples of what it might look like for a student who MEETS EXPECTATIONS, is MAKING PROGRESS, and/or is MAKING LIMITED/NO PROGRESS.

2MD6 Represent Numbers to 100 on a Number Line (b)